diff --git a/src/subtype.c b/src/subtype.c
index 0646f6395a43c..1d169f062ef34 100644
--- a/src/subtype.c
+++ b/src/subtype.c
@@ -1187,7 +1187,7 @@ static jl_value_t *finish_unionall(jl_value_t *res, jl_varbinding_t *vb, jl_sten
     // remove/replace/rewrap free occurrences of this var in the environment
     jl_varbinding_t *btemp = e->vars;
     while (btemp != NULL) {
-        if (jl_has_typevar(btemp->lb, vb->var)) {
+        if (jl_has_typevar(btemp->lb, vb->var) && vb->lb != (jl_value_t*)btemp->var) {
             if (varval)
                 btemp->lb = jl_substitute_var(btemp->lb, vb->var, varval);
             else if (btemp->lb == (jl_value_t*)vb->var)
@@ -1196,7 +1196,7 @@ static jl_value_t *finish_unionall(jl_value_t *res, jl_varbinding_t *vb, jl_sten
                 btemp->lb = jl_new_struct(jl_unionall_type, vb->var, btemp->lb);
             assert((jl_value_t*)btemp->var != btemp->lb);
         }
-        if (jl_has_typevar(btemp->ub, vb->var)) {
+        if (jl_has_typevar(btemp->ub, vb->var) && vb->ub != (jl_value_t*)btemp->var) {
             if (varval)
                 btemp->ub = jl_substitute_var(btemp->ub, vb->var, varval);
             else if (btemp->ub == (jl_value_t*)vb->var)
diff --git a/test/subtype.jl b/test/subtype.jl
index 4ac5347df88d6..502e4130b6a4a 100644
--- a/test/subtype.jl
+++ b/test/subtype.jl
@@ -807,6 +807,11 @@ function test_intersection()
                                               Union{Tuple{S,Array{Int64,1}},Tuple{S,Array{S,1}}} where S),
                               Union{Tuple{Vector{Int64},Vector{Int64}},
                                     Tuple{Vector{T},Vector{T}} where T>:Vector})
+
+    # part of issue #20344
+    @testintersect(Tuple{Type{Tuple{Vararg{T, N} where N}}, Tuple} where T,
+                   Tuple{Type{Tuple{Vararg{T, N}}} where N where T, Any},
+                   Tuple{Type{Tuple{}}, Tuple})
 end
 
 function test_intersection_properties()